Evolutionary topology optimization for temperature reduction of heat conducting fields

This paper aims at developing an efficient finite element based computational procedure for the topology design of heat conducting fields. To evaluate the temperature change in a specific position, due to varying the conducting material distribution in other regions, a discrete temperature sensitivity is derived for an evolutionary topology optimization method. In the topology optimization of the conducting fields, the thermal conductivity of an individual finite element is considered as the design variable. By removing or degenerating the conductive material of the elements with the most negative sensitivity, the temperature objective at the control point can be most efficiently reduced. Illustrative examples are presented to demonstrate this proposed approach.     

TRANSIENT THERMOELASTIC ANALYSIS FOR TWO-DIMENSIONAL DISSIMILAR MATERIALS BY THE BOUNDARY ELEMENT METHOD

This article deals with the transient thermoelastic analysis for dissimilar materials under the plane strain condition. In the process of the boundary element formulation, the time-dependent fundamental solution for the transient heat conduction problem and the thermoelastic displacement potential for the transient thermal stress problem are introduced. Consequently, domain integrals are completely eliminated. The discretization based on the domain combination method for these boundary integral equations is implemented, and the transient temperature and stress fields are analyzed numerically. The transient temperature at the lateral surface and the transient thermal stress at the interface are investigated for the three categories that have been determined according to the characteristic equation expressed by Dundurs parameters.     

小型直喷柴油机传热过程的研究

本文在实测１９０Ａ直喷柴油机缸盖表面瞬态温度的基础上，对该柴油机缸内传热过程进行了分析。利用有限元数值计算方法，针对改变结构设计和冷却方式的不同情况，进行了活塞温度场模拟计算，通过对不同隔热方案和隔热机理进行了研究，为减少该柴油机散热损失提供了理论基础和可行方案。     

TRANSIENT THERMOELASTIC ANALYSIS OF DISK BRAKE USING THE FAST FOURIER TRANSFORM AND FINITE ELEMENT METHOD

This article introduces a finite element method that combines the fast Fourier transform technique and a conventional finite element method as a computational technique for investigating a thermomechanical problem. The conventional finite element formulation is very inefficient in the analysis of a three-dimensional disk brake model of a rotating axisymmetric disk subjected to a nonaxisymmetric transient heat flux condition due to frictional contact with asymmetric pads fixed in space. Because the proposed technique reduces the three-dimensional disk brake mathematics to two dimensions, is an extreme time saver, and costs less, we can solve the transient thermoelastic problem and the thermoelastic instability. As a result of the study we present some analyses on temperature distributions and displacement distributions in a disk brake system at a low speed and on the hot spots at a high speed above critical speed.     

TRANSIENT ANALYSIS OF THERMOELASTIC CONTACT BEHAVIORS IN COMPOSITE MULTIDISK BRAKES

The transient analyses of the thermoelastic contact problem are performed for carbon–carbon composite multidisk brakes subject to mechanical and frictionally excited thermal loads. The finite element method, based on the coupled theory in which displacement and temperature fields are mutually affected, is applied for the numerical simulations. In the present study, to improve the accuracy of computations and stabilize the algorithm, the implicit transient scheme is used for the thermoelastic analysis. The law of action and reaction, Signorini's law of contact, Coulomb's law of friction, and Archard's law of wear are applied to be valid locally at each point for friction surfaces. The computation results are obtained for the antiskid brake conditions and presented for the transient evolution of contact pressure, temperature on each friction surface between the bodies, and thermoelastic deformations. It is also found that the high thermal stresses due to considerable temperature difference during the landing process occur in multidisk brakes.     

Sensitivity analysis in thermoelastic problems using the complex finite element method

This article presents the complex finite element method (ZFEM) for the sensitivity analysis of thermoelastic systems. ZFEM, based on the complex Taylor series approach, performs finite element procedures using complex variables such that the response variables (temperature, stress) and their sensitivities with respect to an input parameter of interest (shape, mechanical and thermal properties, loading) are obtained simultaneously. ZFEM offers significant advantages over alternative sensitivity analyses that require direct derivations of the sensitivity formulae, multiple runs, and/or remeshing. To verify the numerical implementation, a hollow cylinder with convective boundary conditions on the inside and outside surface was considered. First-order derivatives of the stress fields were compared with exact solutions to demonstrate the accuracy of ZFEM sensitivities. The results indicate that the ZFEM-based derivatives are of high accuracy, thereby showing its applicability in the design and analysis of thermoelastic problems.     

TRANSIENT THERMOELASTIC ANALYSIS OF DISK BRAKES IN FRICTIONAL CONTACT

The transient analysis of the thermoelastic contact problem of automotive disk brakes with frictional heat generation is performed using the finite element method. To analyze the thermoelastic phenomenon occurring in disk brakes, the coupled heat conduction and elastic equations are solved with contact problems. In the present work, the fully implicit transient scheme for the thermoelastic analysis is used to improve the accuracy of computations at every time step. The numerical simulation for the thermoelastic behavior of disk brakes is obtained in drag brake condition. The computational results are presented for the distributions of pressure and temperature on each friction surface between the contacting bodies. Also, the thermoelastic instability (TEI) phenomenon (the unstable growth of contact pressure and temperature) is investigated in the present study. The effects of the rotating speed of the disk on thermoelastic behaviors, such as the temperature distribution and contact ratio of the friction surfaces, are investigated.     

Finite Element Analysis of Heat Partition in a Pad/Disc Brake System

The heat partition ratio is an important input parameter in simulation carried out by the finite element method (FEM) of the transient temperature fields in such elements as brakes, a pad, and a disc. Therefore, the aim of this article is to study the influence of nine various (experimental and theoretical) formulas for heat partition ratio on temperature in a pad/disc tribosystem. The real dimensions, operating conditions, and thermophysical properties of materials of two different disc brake systems were adopted for the finite element analysis. The evolutions of the temperature on the contact surface of the pad, obtained for different heat partition ratios, are compared with corresponding experimental data. The results revealed a significant influence of heat partition ratio on the evolution of pad maximal temperature, whereas the disc contact temperature was reasonably stable and coincided with most cases under consideration.     

TRANSIENT THERMOELASTIC PROBLEM FOR AN INFINITE PLATE CONTAINING A PENNY-SHAPED CRACK AT AN ARBITRARY POSITION

This article deals with the transient thermoelastic problem for an infinite plate containing a penny-shaped crack that is parallel to the surfaces of the plate but at an arbitrary position of the plate. The transient thermal stresses are set up by the heat generation on the surfaces and the sudden heat exchange on the surfaces. By using the finite difference method for the time variable, the analytical solution for spatial variables can be obtained. The numerical results for the temperature and stress intensity factor are obtained, and results are shown in graphs.     

Transient Thermoelastic Analysis of a Solid Cylinder Containing a Circumferential Crack Using the C–V Heat Conduction Model

This article presents the transient thermoelastic analysis in a long solid cylinder with a circumferential crack using the C–V heat conduction theory. The outer surface of the cylinder is subjected to a sudden temperature change. The Laplace transform technique is adopted to solve the one-dimensional hyperbolic heat conduction equation, and the axial thermal stress is obtained for the un-cracked cylinder in the Laplace domain. Then this axial thermal stress with a minus sign is applied to the crack surface to form a mixed boundary value problem in the cylindrical coordinate system. A singular integral equation is derived by applying the Fourier and Hankel transforms to solve the mode I crack problem. The transient thermal stress intensity factors are obtained by solving the singular integral equation numerically. The influences of thermal relaxation time, crack geometry, and Biot's number upon transient temperature distributions, axial stress fields, and stress intensity factors are analyzed.     

Transient responses of generalized magnetothermoelasto-diffusive problems with rotation using Laplace transform–finite element method

This article is mainly devoted to the transient response analysis of generalized magnetothermoelasto-diffusive problems with rotation in the context of the generalized thermoelastic diffusion theory. Due to the complexity of governing equations, Laplace transform–finite element method is applied to solve them. As a numerical example, a thermally and electrically conducting rotating half-space whose surface is subjected to a zonal time-dependent thermal and chemical shock is investigated. The transient responses, i.e., dimensionless temperature, chemical potential, displacement as well as stresses, are obtained and illustrated graphically. The parametric studies are performed to evaluate the rotation effect on the transient magnetothermoelasto-diffusive responses.     

Numerical simulation of laser-induced transient temperature field in film-substrate system by finite element method

The transient temperature fields generated by a pulsed laser in film-substrate system are obtained by using the finite element method. Time integrations of the semi-discrete finite element equations are achieved by using approximate one order derivative of temperature. The temperature dependences of material properties are taken into account, which has a great influence on the temperature fields indicated by the numerical results. The pulsed laser-induced transient temperature fields in aluminum/methyl-methacrylate system and aluminum/copper system are obtained, which will be useful in the research on thermoelastic excitation of laser ultrasonic waves in film-substrate system.     

TRANSIENT THERMOELASTIC ANALYSIS OF AN ANNULAR FIN WITH COUPLING EFFECT AND VARIABLE HEAT TRANSFER COEFFICIENT

A hybrid numerical method of the Laplace transformation and the finite difference method is applied to solve the transient thermoelastic problem of an annular fin, in which the thermomechanical coupling effect is taken into account in the governing equation of heat conduction and the heat transfer coefficient is a function of the radius of the fin. The general solutions of the governing equations are first solved in the transform domain. Then the inversion to the real domain is completed via the method of matrix similarity transformation and Fourier series technique. The transient distributions of temperature increment and thermal stresses of the fin in the real domain are calculated numerically. The presented method is more efficient in computing time and is applicable to other types of boundary conditions.     

TWO CRACK GROWTHS IN A FUNCTIONALLY GRADED PLATE UNDER THERMAL SHOCK

This article examines the problem of two thermal cracks under a transient temperature field in a ceramic/metal functionally graded plate. When the functionally graded plate is subjected to thermal shock, multiple cracks often occur on the ceramic surface. It is shown that the crack paths are influenced by interaction between multiple cracks and a compositional profile of the functionally graded plate. Transient thermal stresses are treated as a linear quasi-static thermoelastic problem for a plane strain state. The crack paths of two cracks are obtained using the finite element method with mode I and mode II stress intensity factors.     

Thermally nonlinear generalized thermoelasticity of a layer

This article addresses a clarification study on the thermally nonlinear Fourier/ non-Fourier dynamic coupled (generalized) thermoelasticity. Based on the Maxwell-Cattaneo’s heat conduction law and the infinitesimal theory of thermoelasticity, governing equations for the thermally nonlinear small deformation type of generalized thermoelasticity are derived. The Bubnov–Galerkin scheme is implemented for spatial discretization. The spatially discretized equations are directly discretized in time domain using the fully damped Newmark method. The Newton–Raphson procedure is used to linearize the finite element equations. The layers are exposed to a thermal shock, so that the displacement, temperature, and stress waves propagate in layers. The effects of the time evolution, thermoelastic coupling, and thermal relaxation time on the response of the layers are investigated. Results reveal the significance of the thermally nonlinear analysis of generalized thermoelasticity for the conditions where large temperature elevations exist.     

Thermal fatigue on pistons induced by shaped high power laser. Part II: Design of spatial intensity distribution via numerical simulation

In the laser induced thermal fatigue simulation test on pistons, the high power laser was transformed from the incident Gaussian beam into a concentric multi-circular pattern with specific intensity ratio. The spatial intensity distribution of the shaped beam, which determines the temperature field in the piston, must be designed before a diffractive optical element (DOE) can be manufactured. In this paper, a reverse method based on finite element model (FEM) was proposed to design the intensity distribution in order to simulate the thermal loadings on pistons. Temperature fields were obtained by solving a transient three-dimensional heat conduction equation with convective boundary conditions at the surfaces of the piston workpiece. The numerical model then was validated by approaching the computational results to the experimental data. During the process, some important parameters including laser absorptivity, convective heat transfer coefficient, thermal conductivity and Biot number were also validated. Then, optimization procedure was processed to find favorable spatial intensity distribution for the shaped beam, with the aid of the validated FEM. The analysis shows that the reverse method incorporated with numerical simulation can reduce design cycle and design expense efficiently. This method can serve as a kind of virtual experimental vehicle as well, which makes the thermal fatigue simulation test more controllable and predictable.     

THREE-DIMENSIONAL TRANSIENT THERMAL STRESS ANALYSIS OF A NONHOMOGENEOUS HOLLOW CIRCULAR CYLINDER DUE TO A MOVING HEAT SOURCE IN THE AXIAL DIRECTION

In this paper, a theoretical analysis of a three-dimensional transient thermal stress problem is developed for a nonhomogeneous hollow circular cylinder due to a moving heat source in the axial direction from the inner and /or outer surfaces. Assuming that the hollow circular cylinder has nonhomogeneous thermal and mechanical material properties in the radial direction, the heat conduction problem and the associated thermoelastic behaviors for such nonhomogeneous medium are developed by introducing the theory of laminated composites as one of theoretical approximation. The transient heat conduction problem is treated with the help of the methods of Fourier cosine transformation and Laplace transformation, and the associated thermoelastic field is analyzed making use of the thermoelastic displacement potential, Michell's function, and the Boussinesq's function. Some numerical results for the temperature change and the stress distributions are shown in figures, and the effect of relaxing the thermal stress in the nonhomogeneous hollow circular cylinder and the influence of the velocity of a moving heat source are briefly discussed     

ANALYSIS OF TRANSIENT THERMAL BENDING MOMENTS AND STRESSES OF THE WORKPIECE DURING SURFACE GRINDING

Geometrical inaccuracy is often induced by heat generated during grinding. Furthermore, the transient thermal process is the main cause for the residual stresses on theground surface. The objective of this article is to investigate the three-dimensional transient temperature distribution of the workpiece using the finite difference method,and based on the acquired temperature and beam theory, the thermal moment and thermoelastic stress as calculated using Simpson's multiple numerical integral method. The energypartition is the key factor in accurately predicting the temperature distribution, on which the solution of the thermal moment and stress rely. As the heat conductivity of the workpiece decreases, the stress and moment increase near the wheel-workpiece contact zone and the peaks move closer to the contact position. A smaller thickness results in higher thermal stress and lower thermal moment. Enhancing cooling in grinding effectively reduces temperature and the induced stress.     

Analytical solution of the parabolic and hyperbolic heat transfer equations with constant and transient heat flux conditions on skin tissue

In this article, the parabolic (Pennes bioheat equation) and hyperbolic (thermal wave) bioheat transfer models for constant, periodic and pulse train heat flux boundary conditions are solved analytically by applying the Laplace transform method for skin as a semi-infinite and finite domain. The bioheat transfer analysis with transient heat flux on skin tissue has only been studied by Pennes equation for a semi-infinite domain. For modeling heat transfer in short duration of an initial transient, or when the propagation speed of the thermal wave is finite, there are major differences between the results of parabolic and hyperbolic heat transfer equations. The non-Fourier bioheat transfer equation describes the thermal behavior in the biological tissues better than Fourier equation. The outcome of transient heat flux condition shows that by penetrating into the depths beneath the skin subjected to heat, the amplitude of temperature response decreases significantly. The blood perfusion rate can be predicted using the phase shift between the surface temperature and transient surface heat flux. The thermal damage of the skin is studied by applying both the parabolic and hyperbolic bioheat transfer equations.